We obtain a partial description of the totally geodesic submanifolds of a 2-step, simply connected nilpotent Lie group with a left invariant metric. We consider only the case that N is nonsingular; that is,
ad
ξ
:
N
→
Z
{\text {ad}}\xi :\mathcal {N} \to \mathcal {Z}
is surjective for all elements
ξ
∈
N
−
Z
\xi \in \mathcal {N} - \mathcal {Z}
, where
N
\mathcal {N}
denotes the Lie algebra of N and
Z
\mathcal {Z}
denotes the center of
N
\mathcal {N}
. Among other results we show that if H is a totally geodesic submanifold of N with
dim
H
≥
1
+
dim
Z
\dim H \geq 1 + \dim \mathcal {Z}
, then H is an open subset of
g
N
∗
g{N^\ast }
, where g is an element of H and
N
∗
{N^\ast }
is a totally geodesic subgroup of N. We find simple and useful criteria that are necessary and sufficient for a subalgebra
N
∗
{\mathcal {N}^\ast }
of
N
\mathcal {N}
to be the Lie algebra of a totally geodesic subgroup
N
∗
{N^\ast }
. We define and study the properties of a Gauss map of a totally geodesic submanifold H of N. We conclude with a characterization of 2-step nilpotent Lie groups N of Heisenberg type in terms of the abundance of totally geodesic submanifolds of N.